\( 7 c ^ { 2 } - 7 r + 3 \)

Did you know that the expression \( 7c^2 - 7r + 3 \) can represent a quadratic function in terms of the variable \( c \)? It's neat how the coefficients shape the parabola! Here, \( 7c^2 \) indicates that the parabola opens upwards, because the coefficient of \( c^2 \) is positive. You can explore its vertex and roots using the quadratic formula, which leads to fascinating connections in algebra! Now, if you're looking to factor or simplify this expression, watch out for common mistakes! A common error would be trying to factor out \( 7 \) from all terms without noticing that \( -7r \) cannot be straightforwardly grouped in a nice factored form with \( 7c^2 \). Always keep the variables and their coefficients in mind!